Directed transport within Hamiltonian dynamics: From theory to cold atoms experiments

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This project is aimed at a detailed study of the conditions of emergence, the mechanisms and the control of directed transport at/near the limit of vanishing dissipation (Hamiltonian transport). This task will be undertaken, both in the classical and quantum regimes. Modern progress in the experimental manipulation of ultra-cold atoms in optical lattices constitute an exciting field of topical research, inasmuch as these systems create a direct link between quantum and classical Hamiltonian dynamics. Thus, our planned project is interdisciplinary being settled at the borderline of Hamiltonian chaos, non.equilibrium (quantum)-thermodynamics and quantum optics.In a first part of the project, we plan to elucidate the role of the classical phase space structure in quantum evolution. The specific problem we want to address, is how new transport modes of quantum dynamics may arise due to underlying Hamiltonian mixed phase space, and how these modes can constructively put to use for new schemes of cold-atom manipulations.The second part of the project is devoted to the study of directed transport mechanisms in the case when a ratchet system is subjected to a dephasing environment in the form of heat bath and/or cooperative interactions among different single ratchets. The goal here is to study the role of decoherence in the current rectification processes both, in the semi-classical regime and the quantum regime (coupled quantum ratchets, ratchet with Bose-Einstein condensates).